  
  
  [1XIndex[101X
  
  [2X*[102X, for multiple of ideal of numerical semigroup 7.1-17 
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  [2XAffineSemigroupByEquations[102X 11.1-2 
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  [2XHomogeneousBettiElementsOfNumericalSemigroup[102X 9.5-3 
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  [2XInductiveNumericalSemigroup[102X 5.2-6 
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  [2XIntersectionIdealsOfNumericalSemigroup[102X 7.1-21 
  [2XIntersectionOfNumericalSemigroups[102X 5.2-1 
  [2XIrreducibleMaximalElementsOfGoodSemigroup[102X 12.2-7 
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  [2XIsAffineSemigroupByEquations[102X 11.1-7 
  [2XIsAffineSemigroupByGenerators[102X 11.1-7 
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  [2XIsAperySetAlphaRectangular[102X 6.2-12 
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  [2XIsCyclotomicNumericalSemigroup[102X 10.1-8 
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  [2XIsGenericNumericalSemigroup[102X 4.2-2 
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  [2XIsGradedAssociatedRingNumericalSemigroupBuchsbaum[102X 7.4-2 
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  [2XIsGradedAssociatedRingNumericalSemigroupGorenstein[102X 7.4-7 
  [2XIsIdealOfNumericalSemigroup[102X 7.1-2 
  [2XIsIntegral[102X 7.1-6 
  [2XIsIntegralIdealOfNumericalSemigroup[102X 7.1-6 
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  [2XIsIrreducibleNumericalSemigroup[102X 6.1-1 
  [2XIsKroneckerPolynomial[102X 10.1-7 
  [2XIsListOfIntegersNS[102X A.2-2 
  [2XIsMED[102X 8.1-1 
  [2XIsMEDNumericalSemigroup[102X 8.1-1 
  [2XIsModularNumericalSemigroup[102X 2.2-1 
  [2XIsMonomialNumericalSemigroup[102X 10.2-10 
  [2XIsMpure[102X 7.4-5 
  [2XIsMpureNumericalSemigroup[102X 7.4-5 
  [2XIsNumericalSemigroup[102X 2.2-1 
  [2XIsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity[102X 6.2-8 
  [2XIsNumericalSemigroupByAperyList[102X 2.2-1 
  [2XIsNumericalSemigroupByFundamentalGaps[102X 2.2-1 
  [2XIsNumericalSemigroupByGaps[102X 2.2-1 
  [2XIsNumericalSemigroupByGenerators[102X 2.2-1 
  [2XIsNumericalSemigroupByInterval[102X 2.2-1 
  [2XIsNumericalSemigroupByMinimalGenerators[102X 2.2-1 
  [2XIsNumericalSemigroupByOpenInterval[102X 2.2-1 
  [2XIsNumericalSemigroupBySmallElements[102X 2.2-1 
  [2XIsNumericalSemigroupBySubAdditiveFunction[102X 2.2-1 
  [2XIsNumericalSemigroupPolynomial[102X 10.1-2 
  [2XIsOrdinary[102X, for numerical semigroups 3.1-26 
  [2XIsOrdinaryNumericalSemigroup[102X 3.1-26 
  [2XIsProportionallyModularNumericalSemigroup[102X 2.2-1 
  [2XIsPseudoSymmetric[102X, for numerical semigroups 6.1-3 
  [2XIsPseudoSymmetricNumericalSemigroup[102X 6.1-3 
  [2XIsPure[102X 7.4-6 
  [2XIsPureNumericalSemigroup[102X 7.4-6 
  [2XIsSaturated[102X 8.3-1 
  [2XIsSaturatedNumericalSemigroup[102X 8.3-1 
  [2XIsSelfReciprocalUnivariatePolynomial[102X 10.1-9 
  [2XIsStronglyAdmissiblePattern[102X 7.3-2 
  [2XIsSubsemigroupOfNumericalSemigroup[102X 2.2-5 
  [2XIsSubset[102X 2.2-6 
  [2XIsSuperSymmetricNumericalSemigroup[102X 9.2-18 
  [2XIsSymmetric[102X, for good semigroups 12.3-1 
      for numerical semigroups 6.1-2 
  [2XIsSymmetricGoodSemigroup[102X 12.3-1 
  [2XIsSymmetricNumericalSemigroup[102X 6.1-2 
  [2XIsTelescopic[102X 6.2-6 
  [2XIsTelescopicNumericalSemigroup[102X 6.2-6 
  [2XIsUniquelyPresented[102X 4.2-1 
  [2XIsUniquelyPresentedAffineSemigroup[102X 11.3-8 
  [2XIsUniquelyPresentedNumericalSemigroup[102X 4.2-1 
  [2XIterator[102X, for ideals of numerical semigroups 7.1-15 
      for numerical semigroups 3.1-12 
  [2XKunzCoordinatesOfNumericalSemigroup[102X 3.1-17 
  [2XKunzPolytope[102X 3.1-18 
  [2XLatticePathAssociatedToNumericalSemigroup[102X 3.1-29 
  [2XLengthsOfFactorizationsElementWRTNumericalSemigroup[102X 9.2-2 
  [2XLengthsOfFactorizationsIntegerWRTList[102X 9.2-1 
  [2XLipmanSemigroup[102X 7.2-5 
  [2XLShapesOfNumericalSemigroup[102X 9.1-5 
  [2XMaximalDenumerantOfElementInNumericalSemigroup[102X 9.2-13 
  [2XMaximalDenumerantOfNumericalSemigroup[102X 9.2-15 
  [2XMaximalDenumerantOfSetOfFactorizations[102X 9.2-14 
  [2XMaximalElementsOfGoodSemigroup[102X 12.2-6 
  [2XMaximalIdealOfNumericalSemigroup[102X 7.1-22 
  [2XMaximumDegreeOfElementWRTNumericalSemigroup[102X 9.2-12 
  [2XMEDClosure[102X, for numerical semigroups 8.1-2 
  [2XMEDNumericalSemigroupClosure[102X 8.1-2 
  [2XMicroInvariantsOfNumericalSemigroup[102X 7.2-10 
  [2XMinimalArfGeneratingSystemOfArfNumericalSemigroup[102X 8.2-3 
  [2XMinimalGeneratingSystem[102X, for affine semigroup 11.1-5 
      for ideal of numerical semigroup 7.1-3 
      for numerical semigroup 3.1-2 
  [2XMinimalGeneratingSystemOfIdealOfNumericalSemigroup[102X 7.1-3 
  [2XMinimalGeneratingSystemOfNumericalSemigroup[102X 3.1-2 
  [2XMinimalGenerators[102X 12.2-10 
      for affine semigroup 11.1-5 
      for ideal of numerical semigroup 7.1-3 
      for numerical semigroup 3.1-2 
  [2XMinimalGoodGeneratingSystemOfGoodIdeal[102X 12.4-4 
  [2XMinimalGoodGeneratingSystemOfGoodSemigroup[102X 12.2-9 
  [2XMinimalMEDGeneratingSystemOfMEDNumericalSemigroup[102X 8.1-3 
  [2XMinimalPresentation[102X, for affine semigroup 11.3-4 
      for numerical semigroups 4.1-1 
  [2XMinimalPresentationOfAffineSemigroup[102X 11.3-4 
  [2XMinimalPresentationOfNumericalSemigroup[102X 4.1-1 
  [2XMinimum[102X, minimum of ideal of numerical semigroup 7.1-9 
  [2XModularNumericalSemigroup[102X 2.1-8 
  [2XMoebiusFunctionAssociatedToNumericalSemigroup[102X 9.6-1 
  [2XMonotoneCatenaryDegreeOfAffineSemigroup[102X 11.4-7 
  [2XMonotoneCatenaryDegreeOfNumericalSemigroup[102X 9.3-11 
  [2XMonotoneCatenaryDegreeOfSetOfFactorizations[102X 9.3-4 
  [2XMonotonePrimitiveElementsOfNumericalSemigroup[102X 9.3-10 
  [2XMultipleOfIdealOfNumericalSemigroup[102X 7.1-17 
  [2XMultipleOfNumericalSemigroup[102X 5.2-3 
  [2XMultiplicity[102X, for numerical semigroup 3.1-1 
  [2XMultiplicityOfNumericalSemigroup[102X 3.1-1 
  [2XMultiplicitySequenceOfNumericalSemigroup[102X 7.2-9 
  [2XNextElementOfNumericalSemigroup[102X 3.1-9 
  [2XNumberElement_IdealOfNumericalSemigroup[102X 7.1-12 
  [2XNumberElement_NumericalSemigroup[102X 3.1-11 
  [2XNumericalDuplication[102X 5.2-5 
  [2XNumericalSemigroup[102X, by (closed) interval 2.1-10 
      by affine map 2.1-7 
      by Apery list 2.1-3 
      by fundamental gaps 2.1-6 
      by gaps 2.1-5 
      by generators 2.1-1 
      by modular condition 2.1-8 
      by open interval 2.1-11 
      by proportionally modular condition 2.1-9 
      by small elements 2.1-4 
      by subadditive function 2.1-2 
  [2XNumericalSemigroupByAffineMap[102X 2.1-7 
  [2XNumericalSemigroupByAperyList[102X 2.1-3 
  [2XNumericalSemigroupByFundamentalGaps[102X 2.1-6 
  [2XNumericalSemigroupByGaps[102X 2.1-5 
  [2XNumericalSemigroupByGenerators[102X 2.1-1 
  [2XNumericalSemigroupByInterval[102X 2.1-10 
  [2XNumericalSemigroupByOpenInterval[102X 2.1-11 
  [2XNumericalSemigroupBySmallElements[102X 2.1-4 
  [2XNumericalSemigroupBySubAdditiveFunction[102X 2.1-2 
  [2XNumericalSemigroupDuplication[102X 12.1-2 
  [2XNumericalSemigroupFromNumericalSemigroupPolynomial[102X 10.1-3 
  [2XNumericalSemigroupPolynomial[102X 10.1-1 
  [2XNumericalSemigroupsPlanarSingularityWithFrobeniusNumber[102X 6.2-9 
  [2XNumericalSemigroupsWithFrobeniusNumber[102X 5.4-1 
  [2XNumericalSemigroupsWithGenus[102X 5.5-1 
  [2XNumericalSemigroupsWithPseudoFrobeniusNumbers[102X 5.6-3 
  [2XNumericalSemigroupWithRandomElementsAndFrobenius[102X B.1-6 
  [2XNumSgpsUse4ti2[102X 13.1-1 
  [2XNumSgpsUse4ti2gap[102X 13.1-2 
  [2XNumSgpsUseNormalize[102X 13.1-3 
  [2XNumSgpsUseSingular[102X 13.1-4 
  [2XNumSgpsUseSingularGradedModules[102X 13.1-6 
  [2XNumSgpsUseSingularInterface[102X 13.1-5 
  [2XOmegaPrimalityOfAffineSemigroup[102X 11.4-10 
  [2XOmegaPrimalityOfElementInAffineSemigroup[102X 11.4-9 
  [2XOmegaPrimalityOfElementInNumericalSemigroup[102X 9.4-1 
  [2XOmegaPrimalityOfElementListInNumericalSemigroup[102X 9.4-2 
  [2XOmegaPrimalityOfNumericalSemigroup[102X 9.4-3 
  [2XOverSemigroupsNumericalSemigroup[102X 5.3-1 
  [2XPrimitiveElementsOfAffineSemigroup[102X 11.3-9 
  [2XPrimitiveElementsOfNumericalSemigroup[102X 4.1-4 
  [2XProfileOfNumericalSemigroup[102X 3.2-3 
  [2XProportionallyModularNumericalSemigroup[102X 2.1-9 
  [2XPseudoFrobeniusOfNumericalSemigroup[102X 3.1-22 
  [2XQuotientOfNumericalSemigroup[102X 5.2-2 
  [2XRandomListForNS[102X B.1-2 
  [2XRandomListRepresentingSubAdditiveFunction[102X B.1-5 
  [2XRandomModularNumericalSemigroup[102X B.1-3 
  [2XRandomNumericalSemigroup[102X B.1-1 
  [2XRandomProportionallyModularNumericalSemigroup[102X B.1-4 
  [2XRatliffRushClosureOfIdealOfNumericalSemigroup[102X 7.2-7 
  [2XRatliffRushNumberOfIdealOfNumericalSemigroup[102X 7.2-6 
  [2XRClassesOfSetOfFactorizations[102X 9.1-4 
  [2XReductionNumber[102X, for ideals of numerical semigroups 7.2-3 
  [2XReductionNumberIdealNumericalSemigroup[102X 7.2-3 
  [2XRemoveMinimalGeneratorFromNumericalSemigroup[102X 5.1-1 
  [2XRepresentsGapsOfNumericalSemigroup[102X 2.2-3 
  [2XRepresentsPeriodicSubAdditiveFunction[102X A.2-1 
  [2XRepresentsSmallElementsOfGoodSemigroup[102X 12.2-4 
  [2XRepresentsSmallElementsOfNumericalSemigroup[102X 2.2-2 
  [2XRthElementOfNumericalSemigroup[102X 3.1-6 
  [2XSaturatedClosure[102X, for numerical semigroups 8.3-2 
  [2XSaturatedNumericalSemigroupClosure[102X 8.3-2 
  [2XSaturatedNumericalSemigroupsWithFrobeniusNumber[102X 8.3-3 
  [2XSemigroupOfValuesOfCurve_Global[102X 10.2-7 
  [2XSemigroupOfValuesOfCurve_Local[102X 10.2-6 
  [2XSemigroupOfValuesOfPlaneCurve[102X 10.2-5 
  [2XSemigroupOfValuesOfPlaneCurveWithSinglePlaceAtInfinity[102X 10.2-1 
  [2XSetDotNSEngine[102X 14.1-10 
  [2XShadedSetOfElementInAffineSemigroup[102X 11.3-6 
  [2XShadedSetOfElementInNumericalSemigroup[102X 4.1-5 
  [2XSimpleForcedIntegersForPseudoFrobenius[102X 5.6-2 
  [2XSmallElements[102X, for good ideal 12.4-6 
      for good semigroup 12.2-3 
      for ideal of numerical semigroup 7.1-7 
      for numerical semigroup 3.1-4 
  [2XSmallElementsOfGoodIdeal[102X 12.4-6 
  [2XSmallElementsOfGoodSemigroup[102X 12.2-3 
  [2XSmallElementsOfIdealOfNumericalSemigroup[102X 7.1-7 
  [2XSmallElementsOfNumericalSemigroup[102X 3.1-4 
  [2XSpecialGaps[102X, for numerical semigroup 3.1-32 
  [2XSpecialGapsOfNumericalSemigroup[102X 3.1-32 
  [2XStarClosureOfIdealOfNumericalSemigroup[102X 7.2-13 
  [2XSubtractIdealsOfNumericalSemigroup[102X 7.1-18 
  [2XSumIdealsOfNumericalSemigroup[102X 7.1-16 
  [2XTameDegreeOfAffineSemigroup[102X 11.4-8 
  [2XTameDegreeOfElementInNumericalSemigroup[102X 9.3-13 
  [2XTameDegreeOfNumericalSemigroup[102X 9.3-12 
  [2XTameDegreeOfSetOfFactorizations[102X 9.3-6 
  [2XTelescopicNumericalSemigroupsWithFrobeniusNumber[102X 6.2-7 
  [2XTorsionOfAssociatedGradedRingNumericalSemigroup[102X 7.4-3 
  [2XTranslationOfIdealOfNumericalSemigroup[102X 7.1-20 
  [2XTruncatedWilfNumberOfNumericalSemigroup[102X 3.2-2 
  [2XTypeOfNumericalSemigroup[102X 3.1-23 
  [2XTypeSequenceOfNumericalSemigroup[102X 7.1-25 
  [2XWilfNumber[102X, for numerical semigroup 3.2-1 
  [2XWilfNumberOfNumericalSemigroup[102X 3.2-1 
  
  
  -------------------------------------------------------
